Partial Time-Varying Coefficient Regression and Autoregressive Mixed Model

Regression and autoregressive mixed models are classical models used to analyze the relationship between time series response variable and other covariates. The coefficients in traditional regression and autoregressive mixed models are constants. However, for complicated data, the coefficients of covariates may change with time. In this article, we propose a kind of partial time-varying coefficient regression and autoregressive mixed model and obtain the local weighted least-square estimators of coefficient functions by the local polynomial technique. The asymptotic normality properties of estimators are derived under regularity conditions, and simulation studies are conducted to empirically examine the finite-sample performances of the proposed estimators. Finally, we use real data about Lake Shasta inflow to illustrate the application of the proposed model.

Partial Time-Varying Coefficient Regression and Autoregressive Mixed Model

Regression and autoregressive mixed models are classical models used to analyze the relationship between time series response variable and other covariates. The coefficients in traditional regression and autoregressive mixed models are constants. However, for complicated data, the coefficients of covariates may change with time. In this article, we propose a kind of partial time-varying coefficient regression and autoregressive mixed model and obtain the local weighted least-square estimators of coefficient functions by the local polynomial technique. The asymptotic normality properties of estimators are derived under regularity conditions, and simulation studies are conducted to empirically examine the finite-sample performances of the proposed estimators. Finally, we use real data about Lake Shasta inflow to illustrate the application of the proposed model.

Prediction of different stages of rectal cancer: Texture analysis based on diffusion-weighted images and apparent diffusion coefficient maps

BACKGROUND It is evident that an accurate evaluation of T and N stage rectal cancer is essential for treatment planning.It has not been extensively investigated whether texture features derived from diffusion-weighted imaging(DWI)images and apparent diffusion coefficient(ADC)maps are associated with the extent of local invasion(pathological stage T1-2 vs T3-4)and nodal involvement(pathological stage N0 vs N1-2)in rectal cancer.AIM To predict different stages of rectal cancer using texture analysis based on DWI images and ADC maps.METHODS One hundred and fifteen patients with pathologically proven rectal cancer,who underwent preoperative magnetic resonance imaging,including DWI,were enrolled,retrospectively.The ADC measurements(ADCmean,ADCmin,ADCmax)as well as texture features,including the gray level co-occurrence matrix parameters,the gray level run-length matrix parameters and wavelet parameters were calculated based on DWI(b=0 and b=1000)images and the ADC maps.Independent sample t-tests or Mann-Whitney U tests were used for statistical analysis.Multivariate logistic regression analysis was conducted to establish the models.The predictive performance was validated by receiver operating characteristic curve analysis.RESULTS Dissimilarity,sum average,information correlation and run-length nonuniformity from DWIb=0 images,gray level nonuniformity,run percentage and run-length nonuniformity from DWIb=1000 images,and dissimilarity and run percentage from ADC maps were found to be independent predictors of local invasion(stage T3-4).The area under the operating characteristic curve of the model reached 0.793 with a sensitivity of 78.57%and a specificity of 74.19%.Sum average,gray level nonuniformity and the horizontal components of symlet transform(SymletH)from DWIb=0 images,sum average,information correlation,long run low gray level emphasis and SymletH from DWIb=1000 images,and ADCmax,ADCmean and information correlation from ADC maps were identified as independent predictors of nodal involvement.The area under the operating characteristic curve of the model reached 0.802 with a sensitivity of 80.77%and a specificity of 68.25%.CONCLUSION Texture features extracted from DWI images and ADC maps are useful clues for predicting pathological T and N stages in rectal cancer.

Entropy weight coefficient model and its application in evaluation of groundwater vulnerability of the Sanjiang Plain

The research of groundwater vulnerability is the basic work to protect the groundwater. For utilizing groundwater resource continuably, groundwater vulnerability evaluation is necessary. Useful reference to protect, exploit and utilize on groundwater resource are provided rationally. According to the real condition of Sanjiang Plain, the indexes system is established based on the traditional DRASTIC model. The new system includes the following seven indexes： Depth of Water, Net Recharge, Aquifer Media, Soil Media, Conductivity of the Aquifer, Land Utilizing Ratio and Populace Density. The related analysis appears that the system is rather reasonable. Because traditional methods, such as analytic hierarchy process and fuzzy mathematics theory, can＇t be avoided human interference in selection of weights, they could lead to an imprecise result. In order to evaluate the groundwater vulnerability reasonably, entropy weight coefficient method is applied for the first time, which provides a new way to groundwater vulnerability evaluation. The method is a model whose weights are insured by the calculation process, so the artificial disturb can be avoided. It has been used to evaluate the groundwater vulnerability in Sanjiang Plain. The satisfied result is acquired. Comparably, the same result is acquired by the other method named projection pursuit evaluation based on real-coded accelerating genetic algorithm. It shows that entropy weight coefficient method is applicable on groundwater vulnerability evaluation. The evaluation result can provide reference on the decision-making departments.

GENERAL DECAY FOR A VISCOELASTIC EQUATION OF VARIABLE COEFFICIENTS WITH A TIME-VARYING DELAY IN THE BOUNDARY FEEDBACK AND ACOUSTIC BOUNDARY CONDITIONS

A variable coefficient viscoelastic equation with a time-varying delay in the boundary feedback and acoustic boundary conditions and nonlinear source term is considered.Under suitable assumptions, general decay results of the energy are established via suitable Lyapunov functionals and some properties of the convex functions. Our result is obtained without imposing any restrictive growth assumption on the damping term and the elements of the matrix A and the kernel function g.

Study on Entropy Weight Coefficient Method and Application for Water Quality Evaluation

In order to evaluate the quality of water environment, the conception of entropy is applied in information science, and the entropy weight model is built to evaluate comprehensively water quality. The indexes weights of water quality are determined by value of entropy. This kind of method is applied on evaluating water quality in the new water to be built. The result shows that the water quality in it which supply water is between grade Ⅲ and Ⅳ, and the result is similar to that of gray related method.

Improved calibration method for displacement transformation coefficient in optical and visual measurements

Optical and visual measurement technology is used widely in fields that involve geometric measurements,and among such technology are laser and vision-based displacement measuring modules(LVDMMs).The displacement transformation coefficient(DTC)of an LVDMM changes with the coordinates in the camera image coordinate system during the displacement measuring process,and these changes affect the displacement measurement accuracy of LVDMMs in the full field of view(FFOV).To give LVDMMs higher accuracy in the FFOV and make them adaptable to widely varying measurement demands,a new calibration method is proposed to improve the displacement measurement accuracy of LVDMMs in the FFOV.First,an image coordinate system,a pixel measurement coordinate system,and a displacement measurement coordinate system are established on the laser receiving screen of the LVDMM.In addition,marker spots in the FFOV are selected,and the DTCs at the marker spots are obtained from calibration experiments.Also,a fitting method based on locally weighted scatterplot smoothing(LOWESS)is selected,and with this fitting method the distribution functions of the DTCs in the FFOV are obtained based on the DTCs at the marker spots.Finally,the calibrated distribution functions of the DTCs are applied to the LVDMM,and experiments conducted to verify the displacement measurement accuracies are reported.The results show that the FFOV measurement accuracies for horizontal and vertical displacements are better than±15μm and±19μm,respectively,and that for oblique displacement is better than±24μm.Compared with the traditional calibration method,the displacement measurement error in the FFOV is now 90%smaller.This research on an improved calibration method has certain significance for improving the measurement accuracy of LVDMMs in the FFOV,and it provides a new method and idea for other vision-based fields in which camera parameters must be calibrated.

Apparent diffusion coefficient by diffusion-weighted magnetic resonance imaging as a sole biomarker for staging and prognosis of gastric cancer

Objective： To investigate the role of apparent diffusion coefficient （ADC） from diffusion-weighted magnetic resonance imaging （DW-MRI） when applied to the 7th TNM classification in the staging and prognosis of gastric cancer （GC）. Methods： Between October 2009 and May 2014, a total of 89 patients with non-metastatic, biopsy proven GC underwent 1.5T DW-MRI, and then treated with radical surgery. Tumor ADC was measured retrospectively and compared with final histology following the 7th TNM staging （local invasion, nodal involvement and according to the different groups -- stage Ⅰ, Ⅱ and Ⅲ）. Kaplan-Meier curves were also generated. The follow-up period is updated to May 2016. Results： Median follow-up period was 33 months and 45/89 （51%） deaths from GC were observed. ADC was significantly different both for local invasion and nodal involvement （P〈0.001）. Considering final histology as the reference standard, a preoperative ADC cut-offof 1.80×10-3 mm^2/s could distinguish between stages I and Ⅱ and an ADC value of ≤1.36-10-3 mm^2/s was associated with stage Ⅲ（P〈0.001）. Kaplan-Meier curves demonstrated that the survival rates for the three prognostic groups were significantly different according to final histology and ADC cut-offs （P〈0.001）. Conclusions： ADC is different according to local invasion, nodal involvement and the 7th TNM stage groups for GC, representing a potential, additional prognostic biomarker. The addition of DW-MRI could aid in the staging and risk stratification of GC.

Diffusion-weighted magnetic resonance imaging in cancer: Reported apparent diffusion coefficients,in-vitro and invivo reproducibility

There is considerable disparity in the published apparent diffusion coefficient(ADC) values across different anatomies. Institutions are increasingly assessing repeatability and reproducibility of the derived ADC to determine its variation,which could potentially be used as an indicator in determining tumour aggressiveness or assessing tumour response. In this manuscript,a review of selected articles published to date in healthy extracranial body diffusion-weighted magnetic resonance imaging is presented,detailing reported ADC values and discussing their variation across different studies. In total 115 studies were selected including 28 for liver parenchyma,15 for kidney(renal parenchyma),14 for spleen,13 for pancreatic body,6 for gallbladder,13 for prostate,13 for uterus(endometrium,myometrium,cervix) and 13 for fibroglandular breast tissue. Median ADC values in selected studies were found to be 1.28 × 10-3 mm2/s in liver,1.94 × 10-3 mm2/s in kidney,1.60 × 10-3 mm2/s in pancreatic body,0.85 × 10-3 mm2/s in spleen,2.73 × 10-3 mm2/s in gallbladder,1.64 × 10-3 mm2/s and 1.31 × 10-3 mm2/s in prostate peripheral zone and central gland respectively(combined median value of 1.54×10-3 mm2/s),1.44 × 10-3 mm2/s in endometrium,1.53 × 10-3 mm2/s in myometrium,1.71 × 10-3 mm2/s in cervix and 1.92 × 10-3 mm2/s in breast. In addition,six phantom studies and thirteen in vivo studies were summarized to compare repeatability and reproducibility of the measured ADC. All selected phantom studies demonstrated lower intra-scanner and inter-scanner variation compared to in vivo studies. Based on the findings of this manuscript,it is recommended that protocols need to be optimised for the body part studied and that system-induced variability must be established using a standardized phantom in any clinical study. Reproducibility of the measured ADC must also be assessed in a volunteer population,as variations are far more significant in vivo compared with phantom studies.

ADDITIVE HAZARDS MODEL WITH TIME-VARYING REGRESSION COEFFICIENTS

This article discusses regression analysis of failure time under the additive hazards model, when the regression coefficients are time-varying. The regression coefficients are estimated locally based on the pseudo-score function [12] in a window around each time point. The proposed method can be easily implemented, and the resulting estimators are shown to be consistent and asymptotically normal with easily estimated variances. The simulation studies show that our estimation procedure is reliable and useful.

New computing method of weighted coefficients for tracking a maneuvering target using PDAF in the presence of clutter

To avoid or reduce the influence of unpredictable motion mode on data association, a new computing method of weighted coefficients of measurements for PDAF is presented in which it is assumed that the current turn rate of a maneuvering target changes within a limited range and its turn may be in arbitrary direction during data association. Thus, the predicted center for computing the weighted coefficients is a curved surface in 3-D space, which differs from the predicted center for setting up a validation gate, namely, a point in 3-D space. The distance between a measurement and the curved surface is used to compute its weighted coefficient. To reduce the computational complexity of weighted coefficients, the formulas for computing the maneuvering direction angle and turn rate corresponding to a measurement are presented. Simulation results show the proposed method reduces the percentage of lost tracks and improves the state estimation accuracy in tracking a maneuvering target using PDAF in the presence of clutter.

Feasibility of similarity coefficient map for improving morphological evaluation of T_2* weighted MRI for renal cancer

The purpose of this paper is to investigate the feasibility of using a similarity coefficient map（SCM） in improving the morphological evaluation of T2＊ weighted（T2＊W） magnatic resonance imaging（MRI） for renal cancer.Simulation studies and in vivo 12-echo T2＊W experiments for renal cancers were performed for this purpose.The results of the first simulation study suggest that an SCM can reveal small structures which are hard to distinguish from the background tissue in T2＊W images and the corresponding T2＊ map.The capability of improving the morphological evaluation is likely due to the improvement in the signal-to-noise ratio（SNR） and the carrier-to-noise ratio（CNR） by using the SCM technique.Compared with T2＊ W images,an SCM can improve the SNR by a factor ranging from 1.87 to 2.47.Compared with T2＊ maps,an SCM can improve the SNR by a factor ranging from 3.85 to 33.31.Compared with T2＊W images,an SCM can improve the CNR by a factor ranging from 2.09 to 2.43.Compared with T2＊ maps,an SCM can improve the CNR by a factor ranging from 1.94 to 8.14.For a given noise level,the improvements of the SNR and the CNR depend mainly on the original SNRs and CNRs in T2＊W images,respectively.In vivo experiments confirmed the results of the first simulation study.The results of the second simulation study suggest that more echoes are used to generate the SCM,and higher SNRs and CNRs can be achieved in SCMs.In conclusion,an SCM can provide improved morphological evaluation of T2＊W MR images for renal cancer by unveiling fine structures which are ambiguous or invisible in the corresponding T2＊W MR images and T2＊ maps.Furthermore,in practical applications,for a fixed total sampling time,one should increase the number of echoes as much as possible to achieve SCMs with better SNRs and CNRs.

STUDY ON FREQUENCY ESTIMATION BASED ON WEIGHTED LEAST SQUARE METHOD WITH THREE FOURIER COEFFICIENTS

In this paper,a sinusoidal signal frequency estimation algorithm is proposed by weighted least square method.Based on the idea of Provencher,three biggest Fourier coefficients in the maximum periodogram are considered,the Fourier coefficients can be written as three equations about the amplitude,phase,and frequency,and the frequency is estimated by solving equations.Because of the error of measurement,weighted least square method is used to solve the frequency equation and get the signal frequency.It is shown that the proposed estimator can approach the Cramer-Rao Bound(CRB)with a low Signal-to-Noise Ratio(SNR)threshold and has a higher accuracy.

A Simulation Study on Comparing General Class of Semiparametric Transformation Models for Survival Outcome with Time-Varying Coefficients and Covariates

The consideration of the time-varying covariate and time-varying coefficient effect in survival models are plausible and robust techniques. Such kind of analysis can be carried out with a general class of semiparametric transformation models. The aim of this article is to develop modified estimating equations under semiparametric transformation models of survival time with time-varying coefficient effect and time-varying continuous covariates. For this, it is important to organize the data in a counting process style and transform the time with standard transformation classes which shall be applied in this article. In the situation when the effect of coefficient and covariates change over time, the widely used maximum likelihood estimation method becomes more complex and burdensome in estimating consistent estimates. To overcome this problem, alternatively, the modified estimating equations were applied to estimate the unknown parameters and unspecified monotone transformation functions. The estimating equations were modified to incorporate the time-varying effect in both coefficient and covariates. The performance of the proposed methods is tested through a simulation study. To sum up the study, the effect of possibly time-varying covariates and time-varying coefficients was evaluated in some special cases of semiparametric transformation models. Finally, the results have shown that the role of the time-varying covariate in the semiparametric transformation models was plausible and credible.

A High-Order Conservative Numerical Method for Gross-Pitaevskii Equation with Time-Varying Coefficients in Modeling BEC

We propose a high-order conservative method for the nonlinear Sehodinger/Gross-Pitaevskii equation with time- varying coefficients in modeling Bose Einstein condensation （BEC）. This scheme combined with the sixth-order compact finite difference method and the fourth-order average vector field method, finely describes the condensate wave function and physical characteristics in some small potential wells. Numerical experiments are presented to demonstrate that our numerical scheme is efficient by the comparison with the Fourier pseudo-spectral method. Moreover, it preserves several conservation laws well and even exactly under some specific conditions.

Improvement of Similarity Measure： Pearson Product-Moment Correlation Coefficient

Aim To study the reason of the insensitiveness of Pearson product-momentcorrelation coefficient as a similarity measure and the method to improve its sensitivity. MethodsExperimental and simulated data sets were used. Results The distribution range of the data setsinfluences the sensitivity of Pearson product-moment correlation coefficient. Weighted Pearsonproduct-moment correlation coefficient is more sensitive when the range of the data set is large.Conclusion Weighted Pearson product-moment correlation coefficient is necessary when the range ofthe data set is large.

Apparent diffusion coefficient evaluation for secondary changes in the cerebellum of rats after middle cerebral artery occlusion

Supratentorial cerebral infarction can cause functional inhibition of remote regions such as the cerebellum, which may be relevant to diaschisis. This phenomenon is often analyzed using positron emission tomography and single photon emission CT. However, these methods are expensive and radioactive. Thus, the present study quantified the changes of infarction core and remote regions after unilateral middle cerebral artery occlusion using apparent diffusion coefficient values. Diffu- sion-weighted imaging showed that the area of infarction core gradually increased to involve the cerebral cortex with increasing infarction time. Diffusion weighted imaging signals were initially in- creased and then stabilized by 24 hours. With increasing infarction time, the apparent diffusion co- efficient value in the infarction core and remote bilateral cerebellum both gradually decreased, and then slightly increased 3-24 hours after infarction. Apparent diffusion coefficient values at remote regions （cerebellum） varied along with the change of supratentorial infarction core, suggesting that the phenomenon of diaschisis existed at the remote regions. Thus, apparent diffusion coefficient values and diffusion weighted imaging can be used to detect early diaschisis.

THE COHERENCE COEFFICIENT MAP AND RESIDUE GUIDED LEAST SQUARE PHASE UNWRAPPING ALGORITHM

The generation of high-resolution DEM from interferometric SAR has resulted in the need for accurate and efficient methods of 2-dimensional phase unwrapping. In this paper, we give a brief description of the mathematical base of phase unwrapping, and a detailed description of the unweighted and weighted least square phase unwrapping algorithm.Then our algorithm combining with the weighted least square phase unwrapping guided by the branch-cuts derived from Goldstein’ s algorithm and coherence coefficient map derived from the INSAR data is provided. In our experiment we write subroutines of the Goldstein’s branch-cut algorithm,unweighted and weighted least square phase unwrapping algorithm as well as our algorithm,and construct a small experiment system to resolve the phase unwrapping problem. Finally we test our algorithm on some INSAR data. The result shows that our approach can obtain unwrapped phase correctly and efficiently.

Optimization of Submarine Hydrodynamic Coefficients Based on Immune Genetic Algorithm

Aiming at the demand for optimization of hydrodynamic coefficients in submarine's motion equations,an adaptive weight immune genetic algorithm was proposed to optimize hydrodynamic coefficients in motion equations.Some hydrodynamic coefficients of high sensitivity to control and maneuver were chosen as the optimization objects in the algorithm.By using adaptive weight method to determine the weight and target function,the multi-objective optimization could be translated into single-objective optimization.For a certain kind of submarine,three typical maneuvers were chosen to be the objects of study:overshoot maneuver in horizontal plane,overshoot maneuver in vertical plane and turning circle maneuver in horizontal plane.From the results of computer simulations using primal hydrodynamic coefficient and optimized hydrodynamic coefficient,the efficiency of proposed method is proved.